import pandas as pd
import numpy as np
import igraph as ig
import collections
import matplotlib.pyplot as plt
%matplotlib inline

Explore Data

df_unweighted = pd.read_csv('combined_final_unweighted.csv')
df_unweighted

	node_start	node_end	status
0	Hong Kong	Samoa	jurisdiction
1	Hong Kong	Samoa	jurisdiction
2	Hong Kong	Samoa	jurisdiction
3	Hong Kong	Samoa	jurisdiction
4	Hong Kong	Samoa	jurisdiction
...	...	...	...
338127	Indonesia	British Virgin Islands	officer_base
338128	Cook Islands	British Virgin Islands	officer_base
338129	Hong Kong	British Virgin Islands	officer_base
338130	Cook Islands	United Kingdom	officer_base
338131	Hong Kong	United Kingdom	officer_base

338132 rows × 3 columns

df_weighted = pd.read_csv('combined_final_weighted.csv')
df_weighted

	node_start	node_end	status	weight
0	Hong Kong	Samoa	jurisdiction	2.0
1	Hong Kong	Samoa	jurisdiction	2.0
2	Hong Kong	Samoa	jurisdiction	2.0
3	Hong Kong	Samoa	jurisdiction	2.0
4	Hong Kong	Samoa	jurisdiction	2.0
...	...	...	...	...
338119	Indonesia	British Virgin Islands	officer_base	1.0
338120	Cook Islands	British Virgin Islands	officer_base	1.0
338121	Hong Kong	British Virgin Islands	officer_base	1.0
338122	Cook Islands	United Kingdom	officer_base	1.0
338123	Hong Kong	United Kingdom	officer_base	1.0

338124 rows × 4 columns

df_weighted['status'].unique()

array(['jurisdiction', 'intermediary_base', 'intermediary_jurisdiction',
       'officer_base', 'officer_jurisdiction'], dtype=object)

df_weighted_grouped = pd.read_csv('combined_final_weighted_groupedby.csv')
df_weighted_grouped

	node_start	node_end	weight
0	Albania	Bahamas	4.0
1	Algeria	British Virgin Islands	2.0
2	Algeria	United Kingdom	2.0
3	Algeria	United States	1.0
4	Andorra	Bahamas	52.0
...	...	...	...
2835	Zimbabwe	Hong Kong	3.0
2836	Zimbabwe	Jersey	1.0
2837	Zimbabwe	Panama	6.0
2838	Zimbabwe	Russia	2.0
2839	Zimbabwe	United States	1.0

2840 rows × 3 columns

df_weighted_grouped.describe()

	weight
count	2840.000000
mean	194.889613
std	1729.454201
min	0.500000
25%	2.000000
50%	5.000000
75%	24.000000
max	65366.500000

Convert Data to an Undirected Edge List

# df_jur_grouped_list = df_jur_grouped.values.tolist()
# df_jur_grouped_list

# d = collections.defaultdict(int)
# for n1, n2, v in df_jur_grouped_list:
#     d[min(n1, n2), max(n1, n2)] += v
# result = [[k[0], k[1], v] for k, v in d.items()]

# df_net = pd.DataFrame(result)
# df_net

# df_net = df_net.rename(columns = {0:'node_1', 1:'node_2', 2: 'weight'})
# df_net

#df_net.to_csv('undirected_weighted_grouped.csv', index = False)

# df_net.describe()

Metrics

def get_diameter(community):
    
    diameters = []
    
    for i in range(len(community.subgraphs())):
    
        diameters.append(community.subgraphs()[i].diameter())

    return (diameters)

def get_transitivity(community):
    
    transitivity = []
    
    for i in range(len(community.subgraphs())):
    
        transitivity.append(community.subgraphs()[i].transitivity_undirected())

    return (transitivity)

def get_avg_degree(community):
    
    degree = []
    
    for i in range(len(community.subgraphs())):
    
        degree.append(np.mean(community.subgraphs()[i].degree()))

    return degree

def get_avg_weighted_degree(community):
    
    weighted_degree = []
    
    for i in range(len(community.subgraphs())):
    
        weighted_degree.append(np.mean(community.subgraphs()[i].strength(weights = 'weight')))

    return weighted_degree

All Relationships

Create Graph

g = ig.Graph.TupleList(df_weighted_grouped.itertuples(index=False), directed=True, edge_attrs={'weight': "weight"})

ig.plot(g)

g.diameter()

4

print( "Clustering Coefficient: ", g.transitivity_undirected())

Clustering Coefficient:  0.3859593515919117

np.mean(g.degree())

28.979591836734695

np.mean(g.strength(weights = 'weight'))

5647.821428571428

df_strength = pd.DataFrame({'name': list(g.vs['name']), 'weighted_degree':g.strength(weights = 'weight') } )
df_strength = df_strength.sort_values('weighted_degree', ascending = False).reset_index(drop = True)
df_strength.head(10)

	name	weighted_degree
0	British Virgin Islands	287863.5
1	Hong Kong	113074.5
2	Panama	109901.0
3	Switzerland	77214.5
4	Bahamas	40701.5
5	United Kingdom	38073.5
6	Taiwan	34930.5
7	Seychelles	32602.0
8	Jersey	29869.5
9	China	25281.0

#run cell above before running this always

df_strength['weighted_degree'].plot()
plt.title('Weighted Degree Distribution (All Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Degree')

Text(0, 0.5, 'Weighted Degree')

df_indegree = pd.DataFrame({'name': list(g.vs['name']), 'weighted_indegree':g.strength(weights = 'weight', mode = 'in') } )
df_indegree = df_indegree.sort_values('weighted_indegree', ascending = False).reset_index(drop = True)
df_indegree.head(10)

	name	weighted_indegree
0	British Virgin Islands	280925.0
1	Panama	89885.0
2	Seychelles	31501.5
3	Bahamas	31085.0
4	Niue	18912.0
5	United Kingdom	16320.0
6	Hong Kong	14145.0
7	Samoa	12807.0
8	Russia	10958.0
9	British Anguilla	6480.0

#run cell above before running this always

df_indegree['weighted_indegree'].plot()
plt.title('Weighted In Degree Distribution (All Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted In Degree')

Text(0, 0.5, 'Weighted In Degree')

df_outdegree = pd.DataFrame({'name': list(g.vs['name']), 'weighted_outdegree':g.strength(weights = 'weight', mode = 'out') } )
df_outdegree = df_outdegree.sort_values('weighted_outdegree', ascending = False).reset_index(drop = True)
df_outdegree.head(10)

	name	weighted_outdegree
0	Hong Kong	98929.5
1	Switzerland	76988.5
2	Taiwan	34922.5
3	Jersey	29443.5
4	China	22683.0
5	Luxembourg	21769.5
6	United Kingdom	21753.5
7	Panama	20016.0
8	Singapore	17426.0
9	United States	16818.0

#run cell above before running this always

df_outdegree['weighted_outdegree'].plot()
plt.title('Weighted Out Degree Distribution (All Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Out Degree')

Text(0, 0.5, 'Weighted Out Degree')

df_pagerank = pd.DataFrame({'name': list(g.vs['name']), 'pagerank':g.pagerank(weights = 'weight') } )
df_pagerank = df_pagerank.sort_values('pagerank', ascending = False).reset_index(drop = True)
df_pagerank.head(10)

	name	pagerank
0	British Virgin Islands	0.265045
1	Panama	0.127240
2	Barbados	0.080715
3	Bahamas	0.050056
4	Hong Kong	0.046778
5	United Kingdom	0.046458
6	Seychelles	0.037662
7	Russia	0.032252
8	Niue	0.028310
9	Bermuda	0.016432

#run cell above before running this always

df_pagerank['pagerank'].plot()
plt.title('Pagerank Distribution (All Relationships)')
plt.xlabel('Countries')
plt.ylabel('Pagerank')

Text(0, 0.5, 'Pagerank')

df_authorities = pd.DataFrame({'name': list(g.vs['name']), 'authority_score':g.authority_score(weights = 'weight') } )
df_authorities = df_authorities.sort_values('authority_score', ascending = False).reset_index(drop = True)
df_authorities.head(10)

	name	authority_score
0	British Virgin Islands	1.000000
1	Panama	0.203256
2	Seychelles	0.102670
3	Bahamas	0.068544
4	Samoa	0.063190
5	Niue	0.055153
6	United Kingdom	0.041456
7	Russia	0.028038
8	British Anguilla	0.026740
9	Hong Kong	0.016538

#run cell above before running this always

df_authorities['authority_score'].plot()
plt.title('Authority Score Distribution (All Relationships)')
plt.xlabel('Countries')
plt.ylabel('Authority Score')

Text(0, 0.5, 'Authority Score')

Community Detection

# Define colors used for visualization
colors = ['blue', 'yellow', 'green','purple', 'pink', 'orange', 'lightcoral', 'plum', 'darkgreen', 'darkblue', 'rosybrown',
         'crimson', 'steelblue', 'khaki', 'moccasin', 'orangered', 'fuchsia', 'thistle', 'salmon', 'chocolate', 'lightseagreen',
         'springgreen', 'darkseagreen', 'deeppink', 'mediumvioletred','olive']

Label Propogation Community Detection

comm_lp= g.community_label_propagation(weights = 'weight')

ig.plot(comm_lp, mark_groups = True, layout="drl")

modularity = g.modularity(comm_lp, weights='weight')
print(modularity)

0.0012263425368253737

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_lp))
print('average degree: ', get_avg_degree(comm_lp))
print('transitivity: ', get_transitivity(comm_lp))
print('diameter: ', get_diameter(comm_lp))

average weighted degree:  [0.0, 13304.311688311689, 0.0, 0.0, 84.0, 0.0, 0.0, 18.0, 0.0, 0.0, 230.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 46.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.6657988605818809, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 4, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Leading Eigenvector Community Detection

comm_leading_eigenvector= g.community_leading_eigenvector(weights = 'weight')

ig.plot(comm_leading_eigenvector, mark_groups = True, layout="drl")

/Users/susankoruthu/opt/anaconda3/lib/python3.8/site-packages/igraph/__init__.py:1281: RuntimeWarning: This method was developed for undirected graphs at src/community/leading_eigenvector.c:530
  membership, _, q = GraphBase.community_leading_eigenvector(

modularity = g.modularity(comm_leading_eigenvector, weights='weight')
print(modularity)

0.1503749727369289

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_leading_eigenvector))
print('average degree: ', get_avg_degree(comm_leading_eigenvector))
print('transitivity: ', get_transitivity(comm_leading_eigenvector))
print('diameter: ', get_diameter(comm_leading_eigenvector))

average weighted degree:  [3447.0862068965516, 4977.735042735043, 0.85, 0.0]
average degree:  [8.172413793103448, 24.666666666666668, 0.2, 0.0]
transitivity:  [0.2783573806881243, 0.45566413318856314, nan, nan]
diameter:  [3, 3, 1, 0]

df_leading_eigenvector = pd.DataFrame({'name': list(g.vs['name']), 'community':comm_leading_eigenvector.membership } )
df_leading_eigenvector

	name	community
0	Albania	0
1	Bahamas	0
2	Algeria	1
3	British Virgin Islands	1
4	United Kingdom	1
...	...	...
191	Venezuela	0
192	Vietnam	1
193	Yemen	0
194	Zambia	1
195	Zimbabwe	1

196 rows × 2 columns

df_leading_eigenvector.describe()

	community
count	196.000000
mean	0.816327
std	0.621775
min	0.000000
25%	0.000000
50%	1.000000
75%	1.000000
max	3.000000

df_leading_eigenvector.to_csv('community_detection_csvs_13apr/comm_le_all.csv', index = False)

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_leading_eigenvector.membership)):
    vertex_colors.append(colors[comm_leading_eigenvector.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g,'directed_images/communities_leading_eigenvector.png', vertex_label = g.vs['name'] , **visual_style)

# Set the layout
my_layout = g.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g,'directed_images/leading_vector_circular.png', vertex_label = g.vs['name'] , **visual_style)

for i in range(len(comm_leading_eigenvector.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_leading_eigenvector.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_leading_eigenvector.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_leading_eigenvector.subgraphs()[i],'directed_images/leading_eigenvector_subgraph' + str(i) + '.png' ,vertex_label = comm_leading_eigenvector.subgraphs()[i].vs['name'],**visual_style  )
    

Spinglass Community Detection

comm_spinglass = g.community_spinglass(weights = 'weight')

ig.plot(comm_spinglass, mark_groups = True, layout="drl")

modularity = g.modularity(comm_spinglass, weights='weight')
print(modularity)

0.05390156643282913

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_spinglass))
print('average degree: ', get_avg_degree(comm_spinglass))
print('transitivity: ', get_transitivity(comm_spinglass))
print('diameter: ', get_diameter(comm_spinglass))

average weighted degree:  [2071.3529411764707, 1465.2631578947369, 2549.5555555555557, 313.6, 845.0, 118.26666666666667, 1084.054054054054, 230.0]
average degree:  [3.823529411764706, 4.947368421052632, 15.955555555555556, 2.0, 1.0, 2.4, 3.4594594594594597, 1.0]
transitivity:  [0.1836734693877551, 0.39, 0.5931061806656102, 0.0, nan, 0.1111111111111111, 0.05736677115987461, nan]
diameter:  [4, 3, 3, 1, 1, 3, 3, 1]

df_spinglass = pd.DataFrame({'name': list(g.vs['name']), 'community':comm_spinglass.membership } )
df_spinglass

	name	community
0	Albania	1
1	Bahamas	1
2	Algeria	2
3	British Virgin Islands	6
4	United Kingdom	2
...	...	...
191	Venezuela	0
192	Vietnam	2
193	Yemen	0
194	Zambia	6
195	Zimbabwe	6

196 rows × 2 columns

df_spinglass.describe()

	community
count	196.000000
mean	3.392857
std	2.435580
min	0.000000
25%	1.000000
50%	2.500000
75%	6.000000
max	7.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_spinglass.membership)):
    vertex_colors.append(colors[comm_spinglass.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g,'directed_images/communities_spinglass.png', vertex_label = g.vs['name'] , **visual_style)

# Set the layout
my_layout = g.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g,'directed_images/spinglass_circular.png', vertex_label = g.vs['name'] , **visual_style)

for i in range(len(comm_spinglass.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_spinglass.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_spinglass.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_spinglass.subgraphs()[i],'directed_images/spinglass_subgraph' + str(i) + '.png' ,vertex_label = comm_spinglass.subgraphs()[i].vs['name'],**visual_style  )
    

Walktrap Community Detection

walktrap = g.community_walktrap(weights = 'weight', steps = 2)

comm_walktrap = walktrap.as_clustering()

ig.plot(comm_walktrap, mark_groups = True, layout="drl")

modularity = g.modularity(comm_walktrap, weights='weight')
print(modularity)

0.002050025384918412

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_walktrap))
print('average degree: ', get_avg_degree(comm_walktrap))
print('transitivity: ', get_transitivity(comm_walktrap))
print('diameter: ', get_diameter(comm_walktrap))

average weighted degree:  [0.0, 7984.430656934306, 0.0, 0.0, 143.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 36.90510948905109, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.44463040899562895, nan, nan, 0.0, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

df_walktrap = pd.DataFrame({'name': list(g.vs['name']), 'community':comm_walktrap.membership } )
df_walktrap

	name	community
0	Albania	0
1	Bahamas	1
2	Algeria	2
3	British Virgin Islands	1
4	United Kingdom	1
...	...	...
191	Venezuela	1
192	Vietnam	1
193	Yemen	51
194	Zambia	52
195	Zimbabwe	1

196 rows × 2 columns

df_walktrap.describe()

	community
count	196.000000
mean	7.867347
std	13.652566
min	0.000000
25%	1.000000
50%	1.000000
75%	4.000000
max	52.000000

# ##plot community
# visual_style = {}

# vertex_colors = []

# for i in range(len(comm_walktrap.membership)):
#     vertex_colors.append(colors[comm_walktrap.membership[i]])
    
# # Set bbox and margin
# visual_style["bbox"] = (5000,5000)
# visual_style["margin"] = 17

# # Set vertex colours
# visual_style["vertex_color"] = vertex_colors

# # Set edge width
# visual_style["edge_width"] = np.log(g.es['weight']) + 1

# # Set edge color
# visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# # Set vertex size
# visual_style["vertex_size"] = 15

# # Set vertex label size
# visual_style["vertex_label_size"] = 20

# # Set vertex label color
# visual_style["vertex_label_color"] = 'red'

# # Don't curve the edges
# visual_style["edge_curved"] = False

# # Set the layout
# my_layout = g.layout_fruchterman_reingold()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g,'directed_images/communities_walktrap.png', vertex_label = g.vs['name'] , **visual_style)

# # Set the layout
# my_layout = g.layout_circle()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g,'directed_images/walktrap_circular.png', vertex_label = g.vs['name'] , **visual_style)

# for i in range(len(comm_walktrap.subgraphs())):
    
#     visual_style["bbox"] = (2000,2000)
#     visual_style["margin"] = 17
    
#     # Set vertex colours
#     visual_style["vertex_color"] = 'green'

#     # Set edge width
#     visual_style["edge_width"] = np.log(comm_walktrap.subgraphs()[i].es['weight']) + 1
#     # Set the layout
#     my_layout = comm_walktrap.subgraphs()[i].layout_fruchterman_reingold()
#     visual_style["layout"] = my_layout

#     ig.plot(comm_walktrap.subgraphs()[i],'directed_images/walktrap_subgraph' + str(i) + '.png' ,vertex_label = comm_walktrap.subgraphs()[i].vs['name'],**visual_style  )
    

Infomap Community Detection

comm_infomap = g.community_infomap(edge_weights = 'weight')

ig.plot(comm_infomap, mark_groups = True, layout="drl")

modularity = g.modularity(comm_infomap, weights='weight')
print(modularity)

0.0

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_infomap))
print('average degree: ', get_avg_degree(comm_infomap))
print('transitivity: ', get_transitivity(comm_infomap))
print('diameter: ', get_diameter(comm_infomap))

average weighted degree:  [5647.821428571428]
average degree:  [28.979591836734695]
transitivity:  [0.3859593515919117]
diameter:  [4]

df_infomap = pd.DataFrame({'name': list(g.vs['name']), 'community':comm_infomap.membership } )
df_infomap

	name	community
0	Albania	0
1	Bahamas	0
2	Algeria	0
3	British Virgin Islands	0
4	United Kingdom	0
...	...	...
191	Venezuela	0
192	Vietnam	0
193	Yemen	0
194	Zambia	0
195	Zimbabwe	0

196 rows × 2 columns

All Jurisdictions

df_weighted['status'].unique()

array(['jurisdiction', 'intermediary_base', 'intermediary_jurisdiction',
       'officer_base', 'officer_jurisdiction'], dtype=object)

jurisdiction_list = ['jurisdiction', 'officer_jurisdiction','intermediary jurisdiction']

df_weighted_jur = df_weighted[df_weighted['status'].isin(jurisdiction_list)]
df_jur = df_weighted_jur.drop(['status'], axis = 1)
df_jur

	node_start	node_end	weight
0	Hong Kong	Samoa	2.0
1	Hong Kong	Samoa	2.0
2	Hong Kong	Samoa	2.0
3	Hong Kong	Samoa	2.0
4	Hong Kong	Samoa	2.0
...	...	...	...
221136	Indonesia	Samoa	0.5
221137	Cayman Islands	Samoa	0.5
221138	British Virgin Islands	Samoa	0.5
221139	China	Samoa	0.5
221140	China	British Virgin Islands	0.5

216674 rows × 3 columns

df_jur_grouped = df_jur.groupby(['node_start','node_end'], as_index = False).sum()
df_jur_grouped

	node_start	node_end	weight
0	Albania	Bahamas	4.0
1	Andorra	Bahamas	52.0
2	Andorra	British Virgin Islands	78.0
3	Andorra	Cayman Islands	2.0
4	Andorra	Costa Rica	6.0
...	...	...	...
1222	Vietnam	Panama	2.0
1223	Yemen	Panama	2.0
1224	Zambia	British Virgin Islands	4.0
1225	Zimbabwe	British Virgin Islands	10.0
1226	Zimbabwe	Panama	6.0

1227 rows × 3 columns

Convert Data to an Undirected Edge List

# df_jur_grouped_list = df_jur_grouped.values.tolist()
# df_jur_grouped_list

# d = collections.defaultdict(int)
# for n1, n2, v in df_jur_grouped_list:
#     d[min(n1, n2), max(n1, n2)] += v
# result = [[k[0], k[1], v] for k, v in d.items()]

# df_net = pd.DataFrame(result)
# df_net

# df_net = df_net.rename(columns = {0:'node_1', 1:'node_2', 2: 'weight'})
# df_net

#df_net.to_csv('undirected_weighted_grouped.csv', index = False)

# df_net.describe()

Create Graph

g_aj = ig.Graph.TupleList(df_jur_grouped.itertuples(index=False), directed=True, edge_attrs={'weight': "weight"})

ig.plot(g_aj)

g_aj.diameter()

5

print( "Clustering Coefficient: ", g_aj.transitivity_undirected())

Clustering Coefficient:  0.24745484400656814

np.mean(g_aj.degree())

14.10344827586207

np.mean(g_aj.strength(weights = 'weight'))

4979.028735632184

df_strength = pd.DataFrame({'name': list(g_aj.vs['name']), 'weighted_degree':g_aj.strength(weights = 'weight') } )
df_strength = df_strength.sort_values('weighted_degree', ascending = False).reset_index(drop = True)
df_strength.head(10)

	name	weighted_degree
0	British Virgin Islands	232588.5
1	Panama	104014.0
2	Hong Kong	78953.0
3	Switzerland	76304.0
4	Bahamas	40402.0
5	Seychelles	30510.5
6	Jersey	29128.5
7	Luxembourg	21730.0
8	United Kingdom	20585.0
9	Niue	19422.0

#run cell above before running this always

df_strength['weighted_degree'].plot()
plt.title('Weighted Degree Distribution (All Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Degree')

Text(0, 0.5, 'Weighted Degree')

df_indegree = pd.DataFrame({'name': list(g_aj.vs['name']), 'weighted_indegree':g_aj.strength(weights = 'weight', mode = 'in') } )
df_indegree = df_indegree.sort_values('weighted_indegree', ascending = False).reset_index(drop = True)
df_indegree.head(10)

	name	weighted_indegree
0	British Virgin Islands	229763.0
1	Panama	84486.0
2	Bahamas	31064.0
3	Seychelles	29840.5
4	Niue	18912.0
5	Samoa	12478.5
6	British Anguilla	6480.0
7	Barbados	4722.0
8	Bermuda	4662.0
9	Cayman Islands	2868.0

#run cell above before running this always

df_indegree['weighted_indegree'].plot()
plt.title('Weighted In Degree Distribution (All Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted In Degree')

Text(0, 0.5, 'Weighted In Degree')

df_outdegree = pd.DataFrame({'name': list(g_aj.vs['name']), 'weighted_outdegree':g_aj.strength(weights = 'weight', mode = 'out') } )
df_outdegree = df_outdegree.sort_values('weighted_outdegree', ascending = False).reset_index(drop = True)
df_outdegree.head(10)

	name	weighted_outdegree
0	Hong Kong	77920.0
1	Switzerland	76304.0
2	Jersey	29056.5
3	Luxembourg	21728.0
4	United Kingdom	20391.0
5	Panama	19528.0
6	Guernsey	14800.0
7	United Arab Emirates	14609.5
8	Isle of Man	9988.0
9	United States	9796.5

#run cell above before running this always

df_outdegree['weighted_outdegree'].plot()
plt.title('Weighted Out Degree Distribution (All Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Out Degree')

Text(0, 0.5, 'Weighted Out Degree')

df_pagerank = pd.DataFrame({'name': list(g_aj.vs['name']), 'pagerank':g_aj.pagerank(weights = 'weight') } )
df_pagerank = df_pagerank.sort_values('pagerank', ascending = False).reset_index(drop = True)
df_pagerank.head(10)

	name	pagerank
0	British Virgin Islands	0.241395
1	Barbados	0.173128
2	Panama	0.166709
3	Bahamas	0.063761
4	Seychelles	0.040720
5	Bermuda	0.034410
6	Niue	0.030839
7	British Anguilla	0.022724
8	Cayman Islands	0.019970
9	Samoa	0.016921

#run cell above before running this always

df_pagerank['pagerank'].plot()
plt.title('Pagerank Distribution (All Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Pagerank')

Text(0, 0.5, 'Pagerank')

df_authorities = pd.DataFrame({'name': list(g_aj.vs['name']), 'authority_score':g_aj.authority_score(weights = 'weight') } )
df_authorities = df_authorities.sort_values('authority_score', ascending = False).reset_index(drop = True)
df_authorities.head(10)

	name	authority_score
0	British Virgin Islands	1.000000
1	Panama	0.243957
2	Seychelles	0.112570
3	Bahamas	0.082946
4	Samoa	0.068108
5	Niue	0.066423
6	British Anguilla	0.029361
7	Bermuda	0.011364
8	Cayman Islands	0.006435
9	Nevada	0.004324

#run cell above before running this always

df_authorities['authority_score'].plot()
plt.title('Authority Score Distribution (All Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Authority Score')

Text(0, 0.5, 'Authority Score')

Community Detection

Label Propogation Community Detection

comm_lp_aj= g_aj.community_label_propagation(weights = 'weight')

ig.plot(comm_lp_aj, mark_groups = True, layout="drl")

modularity = g_aj.modularity(comm_lp_aj, weights='weight')
print(modularity)

0.014257837515459181

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_lp_aj))
print('average degree: ', get_avg_degree(comm_lp_aj))
print('transitivity: ', get_transitivity(comm_lp_aj))
print('diameter: ', get_diameter(comm_lp_aj))

average weighted degree:  [0.0, 19364.363636363636, 30.0, 436.2352941176471, 148.0, 0.0, 0.0, 165.33333333333334, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 16.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 14.818181818181818, 1.0, 5.176470588235294, 4.5, 0.0, 0.0, 1.3333333333333333, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.7441300421432872, nan, 0.2608695652173913, 0.5806451612903226, nan, nan, 0.0, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 5, 1, 3, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Leading Eigenvector Community Detection

comm_leading_eigenvector_aj= g_aj.community_leading_eigenvector(weights = 'weight')

ig.plot(comm_leading_eigenvector_aj, mark_groups = True, layout="drl")

/Users/susankoruthu/opt/anaconda3/lib/python3.8/site-packages/igraph/__init__.py:1281: RuntimeWarning: This method was developed for undirected graphs at src/community/leading_eigenvector.c:530
  membership, _, q = GraphBase.community_leading_eigenvector(

modularity = g_aj.modularity(comm_leading_eigenvector_aj, weights='weight')
print(modularity)

0.1392852852192658

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_leading_eigenvector_aj))
print('average degree: ', get_avg_degree(comm_leading_eigenvector_aj))
print('transitivity: ', get_transitivity(comm_leading_eigenvector_aj))
print('diameter: ', get_diameter(comm_leading_eigenvector_aj))

average weighted degree:  [1810.1782178217823, 5338.041095890411]
average degree:  [5.326732673267327, 9.643835616438356]
transitivity:  [0.1493288590604027, 0.3371588523442967]
diameter:  [3, 4]

df_leading_eigenvector_aj= pd.DataFrame({'name': list(g_aj.vs['name']), 'community':comm_leading_eigenvector_aj.membership } )
df_leading_eigenvector_aj

	name	community
0	Albania	0
1	Bahamas	0
2	Andorra	0
3	British Virgin Islands	1
4	Cayman Islands	1
...	...	...
169	Venezuela	0
170	Vietnam	1
171	Yemen	0
172	Zambia	1
173	Zimbabwe	0

174 rows × 2 columns

df_leading_eigenvector_aj.describe()

	community
count	174.000000
mean	0.419540
std	0.494908
min	0.000000
25%	0.000000
50%	0.000000
75%	1.000000
max	1.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_leading_eigenvector_aj.membership)):
    vertex_colors.append(colors[comm_leading_eigenvector_aj.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_aj.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_aj.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_aj,'directed_all_jur_images/communities_leading_eigenvector.png', vertex_label = g_aj.vs['name'] , **visual_style)

# Set the layout
my_layout = g_aj.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_aj,'directed_all_jur_images/leading_vector_circular.png', vertex_label = g_aj.vs['name'] , **visual_style)

for i in range(len(comm_leading_eigenvector_aj.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_leading_eigenvector_aj.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_leading_eigenvector_aj.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_leading_eigenvector_aj.subgraphs()[i],'directed_all_jur_images/leading_eigenvector_subgraph' + str(i) + '.png' ,vertex_label = comm_leading_eigenvector_aj.subgraphs()[i].vs['name'],**visual_style  )
    

Spinglass Community Detection

comm_spinglass_aj = g_aj.community_spinglass(weights = 'weight')

ig.plot(comm_spinglass_aj, mark_groups = True, layout="drl")

modularity = g_aj.modularity(comm_spinglass_aj, weights='weight')
print(modularity)

0.13569283780013383

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_spinglass_aj))
print('average degree: ', get_avg_degree(comm_spinglass_aj))
print('transitivity: ', get_transitivity(comm_spinglass_aj))
print('diameter: ', get_diameter(comm_spinglass_aj))

average weighted degree:  [2847.6545454545453, 105.11111111111111, 844.0, 3140.0, 1567.4871794871794, 659.0]
average degree:  [3.4909090909090907, 2.111111111111111, 1.0, 3.7, 5.384615384615385, 2.5]
transitivity:  [0.09441805225653206, 0.0, nan, 0.12274024738344434, 0.30280373831775703, 0.11392405063291139]
diameter:  [6, 1, 1, 2, 4, 3]

df_spinglass_aj = pd.DataFrame({'name': list(g_aj.vs['name']), 'community':comm_spinglass_aj.membership } )
df_spinglass_aj

	name	community
0	Albania	5
1	Bahamas	5
2	Andorra	3
3	British Virgin Islands	0
4	Cayman Islands	4
...	...	...
169	Venezuela	3
170	Vietnam	4
171	Yemen	3
172	Zambia	0
173	Zimbabwe	0

174 rows × 2 columns

df_spinglass_aj.describe()

	community
count	174.000000
mean	2.287356
std	1.861742
min	0.000000
25%	0.000000
50%	3.000000
75%	4.000000
max	5.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_spinglass_aj.membership)):
    vertex_colors.append(colors[comm_spinglass_aj.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_aj.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_aj.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_aj,'directed_all_jur_images/communities_spinglass.png', vertex_label = g_aj.vs['name'] , **visual_style)

# Set the layout
my_layout = g_aj.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_aj,'directed_all_jur_images/spinglass_circular.png', vertex_label = g_aj.vs['name'] , **visual_style)

for i in range(len(comm_spinglass_aj.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_spinglass_aj.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_spinglass_aj.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_spinglass_aj.subgraphs()[i],'directed_all_jur_images/spinglass_subgraph' + str(i) + '.png' ,vertex_label = comm_spinglass_aj.subgraphs()[i].vs['name'],**visual_style  )
    

Walktrap Community Detection

walktrap_aj = g_aj.community_walktrap(weights = 'weight', steps = 2)

comm_walktrap_aj = walktrap_aj.as_clustering()

ig.plot(comm_walktrap_aj, mark_groups = True, layout="drl")

modularity = g_aj.modularity(comm_walktrap_aj, weights='weight')
print(modularity)

0.003886750362990465

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_walktrap_aj))
print('average degree: ', get_avg_degree(comm_walktrap_aj))
print('transitivity: ', get_transitivity(comm_walktrap_aj))
print('diameter: ', get_diameter(comm_walktrap_aj))

average weighted degree:  [0.0, 6545.106060606061, 0.0, 0.0, 0.0, 0.0, 844.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 17.545454545454547, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.27739790086251687, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

df_walktrap_aj = pd.DataFrame({'name': list(g_aj.vs['name']), 'community':comm_walktrap_aj.membership } )
df_walktrap_aj

	name	community
0	Albania	0
1	Bahamas	1
2	Andorra	1
3	British Virgin Islands	1
4	Cayman Islands	1
...	...	...
169	Venezuela	1
170	Vietnam	1
171	Yemen	40
172	Zambia	41
173	Zimbabwe	1

174 rows × 2 columns

df_walktrap_aj.describe()

	community
count	174.000000
mean	5.735632
std	10.274791
min	0.000000
25%	1.000000
50%	1.000000
75%	1.000000
max	41.000000

# ##plot community
# visual_style = {}

# vertex_colors = []

# for i in range(len(comm_walktrap_aj.membership)):
#     vertex_colors.append(colors[comm_walktrap_aj.membership[i]])
    
# # Set bbox and margin
# visual_style["bbox"] = (5000,5000)
# visual_style["margin"] = 17

# # Set vertex colours
# visual_style["vertex_color"] = vertex_colors

# # Set edge width
# visual_style["edge_width"] = np.log(g_aj.es['weight']) + 1

# # Set edge color
# visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# # Set vertex size
# visual_style["vertex_size"] = 15

# # Set vertex label size
# visual_style["vertex_label_size"] = 20

# # Set vertex label color
# visual_style["vertex_label_color"] = 'red'

# # Don't curve the edges
# visual_style["edge_curved"] = False

# # Set the layout
# my_layout = g_aj.layout_fruchterman_reingold()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_aj,'directed_all_jur_images/communities_walktrap.png', vertex_label = g_aj.vs['name'] , **visual_style)

# # Set the layout
# my_layout = g.layout_circle()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_aj,'directed_all_jur_images/walktrap_circular.png', vertex_label = g_aj.vs['name'] , **visual_style)

# for i in range(len(comm_walktrap_aj.subgraphs())):
    
#     visual_style["bbox"] = (2000,2000)
#     visual_style["margin"] = 17
    
#     # Set vertex colours
#     visual_style["vertex_color"] = 'green'

#     # Set edge width
#     visual_style["edge_width"] = np.log(comm_walktrap_aj.subgraphs()[i].es['weight']) + 1
#     # Set the layout
#     my_layout = comm_walktrap_aj.subgraphs()[i].layout_fruchterman_reingold()
#     visual_style["layout"] = my_layout

#     ig.plot(comm_walktrap_aj.subgraphs()[i],'directed_all_jur_images/walktrap_subgraph' + str(i) + '.png' ,vertex_label = comm_walktrap_aj.subgraphs()[i].vs['name'],**visual_style  )
    

Infomap Community Detection

comm_infomap_aj = g_aj.community_infomap(edge_weights = 'weight')

ig.plot(comm_infomap_aj, mark_groups = True, layout="drl")

modularity = g_aj.modularity(comm_infomap_aj, weights='weight')
print(modularity)

0.0

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_infomap_aj))
print('average degree: ', get_avg_degree(comm_infomap_aj))
print('transitivity: ', get_transitivity(comm_infomap_aj))
print('diameter: ', get_diameter(comm_infomap_aj))

average weighted degree:  [4979.028735632184]
average degree:  [14.10344827586207]
transitivity:  [0.24745484400656814]
diameter:  [5]

df_infomap_aj = pd.DataFrame({'name': list(g_aj.vs['name']), 'community':comm_infomap_aj.membership } )
df_infomap_aj

	name	community
0	Albania	0
1	Bahamas	0
2	Andorra	0
3	British Virgin Islands	0
4	Cayman Islands	0
...	...	...
169	Venezuela	0
170	Vietnam	0
171	Yemen	0
172	Zambia	0
173	Zimbabwe	0

174 rows × 2 columns

Only Jurisdiction

df_weighted['status'].unique()

array(['jurisdiction', 'intermediary_base', 'intermediary_jurisdiction',
       'officer_base', 'officer_jurisdiction'], dtype=object)

jurisdiction_list = ['jurisdiction']

df_weighted_jur = df_weighted[df_weighted['status'].isin(jurisdiction_list)]
df_jur = df_weighted_jur.drop(['status'], axis = 1)
df_jur

	node_start	node_end	weight
0	Hong Kong	Samoa	2.0
1	Hong Kong	Samoa	2.0
2	Hong Kong	Samoa	2.0
3	Hong Kong	Samoa	2.0
4	Hong Kong	Samoa	2.0
...	...	...	...
216554	British Virgin Islands	Cook Islands	2.0
216555	British Virgin Islands	Cook Islands	2.0
216556	British Virgin Islands	Cook Islands	2.0
216557	British Virgin Islands	Cook Islands	2.0
216558	Vanuatu	Cook Islands	2.0

216559 rows × 3 columns

df_jur_grouped = df_jur.groupby(['node_start','node_end'], as_index = False).sum()
df_jur_grouped

	node_start	node_end	weight
0	Albania	Bahamas	4.0
1	Andorra	Bahamas	52.0
2	Andorra	British Virgin Islands	78.0
3	Andorra	Cayman Islands	2.0
4	Andorra	Costa Rica	6.0
...	...	...	...
1212	Vietnam	Panama	2.0
1213	Yemen	Panama	2.0
1214	Zambia	British Virgin Islands	4.0
1215	Zimbabwe	British Virgin Islands	10.0
1216	Zimbabwe	Panama	6.0

1217 rows × 3 columns

Convert Data to an Undirected Edge List

# df_jur_grouped_list = df_jur_grouped.values.tolist()
# df_jur_grouped_list

# d = collections.defaultdict(int)
# for n1, n2, v in df_jur_grouped_list:
#     d[min(n1, n2), max(n1, n2)] += v
# result = [[k[0], k[1], v] for k, v in d.items()]

# df_net = pd.DataFrame(result)
# df_net

# df_net = df_net.rename(columns = {0:'node_1', 1:'node_2', 2: 'weight'})
# df_net

#df_net.to_csv('undirected_weighted_grouped.csv', index = False)

# df_net.describe()

Create Graph

g_j = ig.Graph.TupleList(df_jur_grouped.itertuples(index=False), directed=True, edge_attrs={'weight': "weight"})

ig.plot(g_j)

g_j.diameter()

5

print( "Clustering Coefficient: ", g_j.transitivity_undirected())

Clustering Coefficient:  0.24672505151604357

np.mean(g_j.degree())

13.988505747126437

np.mean(g_j.strength(weights = 'weight'))

4978.367816091954

df_strength = pd.DataFrame({'name': list(g_j.vs['name']), 'weighted_degree':g_j.strength(weights = 'weight') } )
df_strength = df_strength.sort_values('weighted_degree', ascending = False).reset_index(drop = True)
df_strength

	name	weighted_degree
0	British Virgin Islands	232540.0
1	Panama	104014.0
2	Hong Kong	78946.0
3	Switzerland	76304.0
4	Bahamas	40402.0
...	...	...
169	Malawi	2.0
170	Nauru	2.0
171	Sudan	2.0
172	Saint Martin (French part)	2.0
173	Guam	2.0

174 rows × 2 columns

df_strength = pd.DataFrame({'name': list(g_j.vs['name']), 'weighted_degree':g_j.strength(weights = 'weight') } )
df_strength = df_strength.sort_values('weighted_degree', ascending = False).reset_index(drop = True)
df_strength.head(10)

	name	weighted_degree
0	British Virgin Islands	232540.0
1	Panama	104014.0
2	Hong Kong	78946.0
3	Switzerland	76304.0
4	Bahamas	40402.0
5	Seychelles	30510.0
6	Jersey	29128.0
7	Luxembourg	21730.0
8	United Kingdom	20584.0
9	Niue	19422.0

#run cell above before running this always

df_strength['weighted_degree'].plot()
plt.title('Weighted Degree Distribution (Only Jurisdiction Relationship)')
plt.xlabel('Countries')
plt.ylabel('Weighted Degree')

Text(0, 0.5, 'Weighted Degree')

df_indegree = pd.DataFrame({'name': list(g_j.vs['name']), 'weighted_indegree':g_j.strength(weights = 'weight', mode = 'in') } )
df_indegree = df_indegree.sort_values('weighted_indegree', ascending = False).reset_index(drop = True)
df_indegree.head(10)

	name	weighted_indegree
0	British Virgin Islands	229716.0
1	Panama	84486.0
2	Bahamas	31064.0
3	Seychelles	29840.0
4	Niue	18912.0
5	Samoa	12474.0
6	British Anguilla	6480.0
7	Barbados	4722.0
8	Bermuda	4662.0
9	Cayman Islands	2868.0

#run cell above before running this always

df_indegree['weighted_indegree'].plot()
plt.title('Weighted In Degree Distribution (Only Jurisdiction Relationship)')
plt.xlabel('Countries')
plt.ylabel('Weighted In Degree')

Text(0, 0.5, 'Weighted In Degree')

df_outdegree = pd.DataFrame({'name': list(g_j.vs['name']), 'weighted_outdegree':g_j.strength(weights = 'weight', mode = 'out') } )
df_outdegree = df_outdegree.sort_values('weighted_outdegree', ascending = False).reset_index(drop = True)
df_outdegree.head(10)

	name	weighted_outdegree
0	Hong Kong	77914.0
1	Switzerland	76304.0
2	Jersey	29056.0
3	Luxembourg	21728.0
4	United Kingdom	20390.0
5	Panama	19528.0
6	Guernsey	14800.0
7	United Arab Emirates	14608.0
8	Isle of Man	9988.0
9	United States	9792.0

#run cell above before running this always

df_outdegree['weighted_outdegree'].plot()
plt.title('Weighted Out Degree Distribution (Only Jurisdiction Relationship)')
plt.xlabel('Countries')
plt.ylabel('Weighted Out Degree')

Text(0, 0.5, 'Weighted Out Degree')

df_pagerank = pd.DataFrame({'name': list(g_j.vs['name']), 'pagerank':g_j.pagerank(weights = 'weight') } )
df_pagerank = df_pagerank.sort_values('pagerank', ascending = False).reset_index(drop = True)
df_pagerank.head(10)

	name	pagerank
0	British Virgin Islands	0.241222
1	Barbados	0.173126
2	Panama	0.166738
3	Bahamas	0.063767
4	Seychelles	0.040682
5	Bermuda	0.034434
6	Niue	0.030858
7	British Anguilla	0.022747
8	Cayman Islands	0.019978
9	Samoa	0.016894

#run cell above before running this always

df_pagerank['pagerank'].plot()
plt.title('Pagerank Distribution (Only Jurisdiction Relationship)')
plt.xlabel('Countries')
plt.ylabel('Pagerank')

Text(0, 0.5, 'Pagerank')

df_authorities = pd.DataFrame({'name': list(g_j.vs['name']), 'authority_score':g_j.authority_score(weights = 'weight') } )
df_authorities = df_authorities.sort_values('authority_score', ascending = False).reset_index(drop = True)
df_authorities.head(10)

	name	authority_score
0	British Virgin Islands	1.000000
1	Panama	0.243992
2	Seychelles	0.112577
3	Bahamas	0.082955
4	Samoa	0.068108
5	Niue	0.066430
6	British Anguilla	0.029362
7	Bermuda	0.011364
8	Cayman Islands	0.006434
9	Nevada	0.004324

#run cell above before running this always

df_authorities['authority_score'].plot()
plt.title('Authority Score Distribution (Only Jurisdiction Relationship)')
plt.xlabel('Countries')
plt.ylabel('Authority Score')

Text(0, 0.5, 'Authority Score')

Community Detection

Label Propogation Community Detection

comm_lp_j= g_j.community_label_propagation(weights = 'weight')

ig.plot(comm_lp_j, mark_groups = True, layout="drl")

modularity = g_j.modularity(comm_lp_j, weights='weight')
print(modularity)

0.017876015599913773

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_lp_j))
print('average degree: ', get_avg_degree(comm_lp_j))
print('transitivity: ', get_transitivity(comm_lp_j))
print('diameter: ', get_diameter(comm_lp_j))

average weighted degree:  [0.0, 23828.470588235294, 30.0, 467.45454545454544, 147.5, 0.0, 0.0, 18.0, 0.0, 0.0, 0.0, 230.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 16.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 14.0, 1.0, 6.0, 4.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.8377581120943953, nan, 0.33994334277620397, 0.5142857142857142, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 3, 1, 4, 3, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Leading Eigenvector Community Detection

comm_leading_eigenvector_j= g_j.community_leading_eigenvector(weights = 'weight')

ig.plot(comm_leading_eigenvector_j, mark_groups = True, layout="drl")

/Users/susankoruthu/opt/anaconda3/lib/python3.8/site-packages/igraph/__init__.py:1281: RuntimeWarning: This method was developed for undirected graphs at src/community/leading_eigenvector.c:530
  membership, _, q = GraphBase.community_leading_eigenvector(

modularity = g_j.modularity(comm_leading_eigenvector_j, weights='weight')
print(modularity)

0.13928311330179288

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_leading_eigenvector_j))
print('average degree: ', get_avg_degree(comm_leading_eigenvector_j))
print('transitivity: ', get_transitivity(comm_leading_eigenvector_j))
print('diameter: ', get_diameter(comm_leading_eigenvector_j))

average weighted degree:  [1792.4313725490197, 5410.888888888889]
average degree:  [5.2745098039215685, 9.61111111111111]
transitivity:  [0.1493288590604027, 0.33534222987516143]
diameter:  [3, 4]

df_leading_eigenvector_j= pd.DataFrame({'name': list(g_j.vs['name']), 'community':comm_leading_eigenvector_j.membership } )
df_leading_eigenvector_j

	name	community
0	Albania	0
1	Bahamas	0
2	Andorra	0
3	British Virgin Islands	1
4	Cayman Islands	1
...	...	...
169	Venezuela	0
170	Vietnam	1
171	Yemen	0
172	Zambia	1
173	Zimbabwe	0

174 rows × 2 columns

df_leading_eigenvector_j.describe()

	community
count	174.000000
mean	0.413793
std	0.493934
min	0.000000
25%	0.000000
50%	0.000000
75%	1.000000
max	1.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_leading_eigenvector_j.membership)):
    vertex_colors.append(colors[comm_leading_eigenvector_j.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_j.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_j.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_j,'directed_all_jur_images/communities_leading_eigenvector.png', vertex_label = g_j.vs['name'] , **visual_style)

# Set the layout
my_layout = g_j.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_j,'directed_all_jur_images/leading_vector_circular.png', vertex_label = g_j.vs['name'] , **visual_style)

for i in range(len(comm_leading_eigenvector_j.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_leading_eigenvector_j.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_leading_eigenvector_j.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_leading_eigenvector_j.subgraphs()[i],'directed_all_jur_images/leading_eigenvector_subgraph' + str(i) + '.png' ,vertex_label = comm_leading_eigenvector_j.subgraphs()[i].vs['name'],**visual_style  )
    

Spinglass Community Detection

comm_spinglass_j = g_j.community_spinglass(weights = 'weight')

ig.plot(comm_spinglass_j, mark_groups = True, layout="drl")

modularity = g_j.modularity(comm_spinglass_j, weights='weight')
print(modularity)

0.10736202089136093

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_spinglass_j))
print('average degree: ', get_avg_degree(comm_spinglass_j))
print('transitivity: ', get_transitivity(comm_spinglass_j))
print('diameter: ', get_diameter(comm_spinglass_j))

average weighted degree:  [1556.6, 125.0, 145.6, 5716.279069767442, 519.0, 1353.3617021276596]
average degree:  [5.4, 1.5, 2.1, 3.953488372093023, 2.4, 3.1914893617021276]
transitivity:  [0.29261862917398945, 0.0, 0.0, 0.1848101265822785, 0.07142857142857142, 0.08368554522400676]
diameter:  [4, 2, 1, 6, 3, 2]

df_spinglass_j = pd.DataFrame({'name': list(g_j.vs['name']), 'community':comm_spinglass_j.membership } )
df_spinglass_j

	name	community
0	Albania	4
1	Bahamas	4
2	Andorra	5
3	British Virgin Islands	3
4	Cayman Islands	0
...	...	...
169	Venezuela	5
170	Vietnam	0
171	Yemen	5
172	Zambia	3
173	Zimbabwe	5

174 rows × 2 columns

df_spinglass_j.describe()

	community
count	174.000000
mean	2.804598
std	1.858205
min	0.000000
25%	1.250000
50%	3.000000
75%	5.000000
max	5.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_spinglass_j.membership)):
    vertex_colors.append(colors[comm_spinglass_j.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_j.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_j.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_j,'directed_all_jur_images/communities_spinglass.png', vertex_label = g_j.vs['name'] , **visual_style)

# Set the layout
my_layout = g_j.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_j,'directed_all_jur_images/spinglass_circular.png', vertex_label = g_j.vs['name'] , **visual_style)

for i in range(len(comm_spinglass_j.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_spinglass_j.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_spinglass_j.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_spinglass_j.subgraphs()[i],'directed_all_jur_images/spinglass_subgraph' + str(i) + '.png' ,vertex_label = comm_spinglass_j.subgraphs()[i].vs['name'],**visual_style  )
    

Walktrap Community Detection

walktrap_j = g_j.community_walktrap(weights = 'weight', steps = 2)

comm_walktrap_j = walktrap_j.as_clustering()

ig.plot(comm_walktrap_j, mark_groups = True, layout="drl")

modularity = g_j.modularity(comm_walktrap_j, weights='weight')
print(modularity)

0.003887288169812182

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_walktrap_j))
print('average degree: ', get_avg_degree(comm_walktrap_j))
print('transitivity: ', get_transitivity(comm_walktrap_j))
print('diameter: ', get_diameter(comm_walktrap_j))

average weighted degree:  [0.0, 6544.272727272727, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 844.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 17.439393939393938, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.27605592593366635, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

df_walktrap_j = pd.DataFrame({'name': list(g_j.vs['name']), 'community':comm_walktrap_j.membership } )
df_walktrap_j

	name	community
0	Albania	0
1	Bahamas	1
2	Andorra	1
3	British Virgin Islands	1
4	Cayman Islands	1
...	...	...
169	Venezuela	1
170	Vietnam	1
171	Yemen	40
172	Zambia	41
173	Zimbabwe	1

174 rows × 2 columns

df_walktrap_j.describe()

	community
count	174.000000
mean	5.764368
std	10.282523
min	0.000000
25%	1.000000
50%	1.000000
75%	1.000000
max	41.000000

# ##plot community
# visual_style = {}

# vertex_colors = []

# for i in range(len(comm_walktrap_j.membership)):
#     vertex_colors.append(colors[comm_walktrap_j.membership[i]])
    
# # Set bbox and margin
# visual_style["bbox"] = (5000,5000)
# visual_style["margin"] = 17

# # Set vertex colours
# visual_style["vertex_color"] = vertex_colors

# # Set edge width
# visual_style["edge_width"] = np.log(g_j.es['weight']) + 1

# # Set edge color
# visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# # Set vertex size
# visual_style["vertex_size"] = 15

# # Set vertex label size
# visual_style["vertex_label_size"] = 20

# # Set vertex label color
# visual_style["vertex_label_color"] = 'red'

# # Don't curve the edges
# visual_style["edge_curved"] = False

# # Set the layout
# my_layout = g_j.layout_fruchterman_reingold()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_j,'directed_all_jur_images/communities_walktrap.png', vertex_label = g_j.vs['name'] , **visual_style)

# # Set the layout
# my_layout = g_j.layout_circle()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_j,'directed_all_jur_images/walktrap_circular.png', vertex_label = g_j.vs['name'] , **visual_style)

# for i in range(len(comm_walktrap_j.subgraphs())):
    
#     visual_style["bbox"] = (2000,2000)
#     visual_style["margin"] = 17
    
#     # Set vertex colours
#     visual_style["vertex_color"] = 'green'

#     # Set edge width
#     visual_style["edge_width"] = np.log(comm_walktrap_j.subgraphs()[i].es['weight']) + 1
#     # Set the layout
#     my_layout = comm_walktrap_j.subgraphs()[i].layout_fruchterman_reingold()
#     visual_style["layout"] = my_layout

#     ig.plot(comm_walktrap_j.subgraphs()[i],'directed_all_jur_images/walktrap_subgraph' + str(i) + '.png' ,vertex_label = comm_walktrap_j.subgraphs()[i].vs['name'],**visual_style  )
    

Infomap Community Detection

comm_infomap_j = g_j.community_infomap(edge_weights = 'weight')

ig.plot(comm_infomap_j, mark_groups = True, layout="drl")

modularity = g_j.modularity(comm_infomap_j, weights='weight')
print(modularity)

0.0

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_infomap_j))
print('average degree: ', get_avg_degree(comm_infomap_j))
print('transitivity: ', get_transitivity(comm_infomap_j))
print('diameter: ', get_diameter(comm_infomap_j))

average weighted degree:  [4978.367816091954]
average degree:  [13.988505747126437]
transitivity:  [0.24672505151604357]
diameter:  [5]

df_infomap_j = pd.DataFrame({'name': list(g_j.vs['name']), 'community':comm_infomap_j.membership } )
df_infomap_j

	name	community
0	Albania	0
1	Bahamas	0
2	Andorra	0
3	British Virgin Islands	0
4	Cayman Islands	0
...	...	...
169	Venezuela	0
170	Vietnam	0
171	Yemen	0
172	Zambia	0
173	Zimbabwe	0

174 rows × 2 columns

Officer Jurisdiction

df_weighted['status'].unique()

array(['jurisdiction', 'intermediary_base', 'intermediary_jurisdiction',
       'officer_base', 'officer_jurisdiction'], dtype=object)

jurisdiction_list = ['officer_jurisdiction']

df_weighted_jur = df_weighted[df_weighted['status'].isin(jurisdiction_list)]
df_jur = df_weighted_jur.drop(['status'], axis = 1)
df_jur

	node_start	node_end	weight
221026	Jersey	British Virgin Islands	0.5
221027	China	British Virgin Islands	0.5
221028	China	British Virgin Islands	0.5
221029	United States	British Virgin Islands	0.5
221030	Indonesia	British Virgin Islands	0.5
...	...	...	...
221136	Indonesia	Samoa	0.5
221137	Cayman Islands	Samoa	0.5
221138	British Virgin Islands	Samoa	0.5
221139	China	Samoa	0.5
221140	China	British Virgin Islands	0.5

115 rows × 3 columns

df_jur_grouped = df_jur.groupby(['node_start','node_end'], as_index = False).sum()
df_jur_grouped

	node_start	node_end	weight
0	British Virgin Islands	Cook Islands	0.5
1	British Virgin Islands	Samoa	0.5
2	British Virgin Islands	Seychelles	0.5
3	Canada	British Virgin Islands	0.5
4	Cayman Islands	British Virgin Islands	0.5
5	Cayman Islands	Samoa	0.5
6	China	British Virgin Islands	7.5
7	China	Labuan	0.5
8	China	Samoa	1.0
9	China	Singapore	0.5
10	Czech Republic	British Virgin Islands	0.5
11	Fiji	British Virgin Islands	0.5
12	Hong Kong	British Virgin Islands	6.0
13	India	British Virgin Islands	2.0
14	India	Samoa	0.5
15	Indonesia	British Virgin Islands	4.5
16	Indonesia	Samoa	0.5
17	Italy	Cook Islands	0.5
18	Japan	British Virgin Islands	1.0
19	Jersey	British Virgin Islands	0.5
20	Macao	Cook Islands	0.5
21	Malaysia	British Virgin Islands	1.0
22	Monaco	British Virgin Islands	0.5
23	New Zealand	British Virgin Islands	0.5
24	Philippines	British Virgin Islands	1.0
25	Romania	British Virgin Islands	0.5
26	Samoa	British Virgin Islands	0.5
27	Singapore	British Virgin Islands	1.5
28	Singapore	Hong Kong	0.5
29	Singapore	Samoa	0.5
30	South Korea	British Virgin Islands	0.5
31	Taiwan	British Virgin Islands	11.0
32	Taiwan	Hong Kong	0.5
33	Taiwan	Labuan	0.5
34	Taiwan	Samoa	0.5
35	Thailand	Samoa	0.5
36	US Virgin Islands	British Virgin Islands	0.5
37	US Virgin Islands	Singapore	0.5
38	United Arab Emirates	British Virgin Islands	1.5
39	United Kingdom	British Virgin Islands	1.0
40	United States	British Virgin Islands	3.5
41	United States	Cook Islands	1.0

Convert Data to an Undirected Edge List

# df_jur_grouped_list = df_jur_grouped.values.tolist()
# df_jur_grouped_list

# d = collections.defaultdict(int)
# for n1, n2, v in df_jur_grouped_list:
#     d[min(n1, n2), max(n1, n2)] += v
# result = [[k[0], k[1], v] for k, v in d.items()]

# df_net = pd.DataFrame(result)
# df_net

# df_net = df_net.rename(columns = {0:'node_1', 1:'node_2', 2: 'weight'})
# df_net

#df_net.to_csv('undirected_weighted_grouped.csv', index = False)

# df_net.describe()

Create Graph

g_oj = ig.Graph.TupleList(df_jur_grouped.itertuples(index=False), directed=True, edge_attrs={'weight': "weight"})

ig.plot(g_oj)

g_oj.diameter()

3

print( "Clustering Coefficient: ", g_oj.transitivity_undirected())

Clustering Coefficient:  0.09863013698630137

np.mean(g_oj.degree())

2.8

np.mean(g_oj.strength(weights = 'weight'))

3.8333333333333335

df_strength = pd.DataFrame({'name': list(g_oj.vs['name']), 'weighted_degree':g_oj.strength(weights = 'weight') } )
df_strength = df_strength.sort_values('weighted_degree', ascending = False).reset_index(drop = True)
df_strength.head(10)

	name	weighted_degree
0	British Virgin Islands	48.5
1	Taiwan	12.5
2	China	9.5
3	Hong Kong	7.0
4	Samoa	5.0
5	Indonesia	5.0
6	United States	4.5
7	Singapore	3.5
8	Cook Islands	2.5
9	India	2.5

#run cell above before running this always

df_strength['weighted_degree'].plot()
plt.title('Weighted Degree Distribution (Officer Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Degree')

Text(0, 0.5, 'Weighted Degree')

df_indegree = pd.DataFrame({'name': list(g_oj.vs['name']), 'weighted_indegree':g_oj.strength(weights = 'weight', mode = 'in') } )
df_indegree = df_indegree.sort_values('weighted_indegree', ascending = False).reset_index(drop = True)
df_indegree.head(10)

	name	weighted_indegree
0	British Virgin Islands	47.0
1	Samoa	4.5
2	Cook Islands	2.5
3	Hong Kong	1.0
4	Labuan	1.0
5	Singapore	1.0
6	Seychelles	0.5
7	New Zealand	0.0
8	Philippines	0.0
9	Romania	0.0

#run cell above before running this always

df_indegree['weighted_indegree'].plot()
plt.title('Weighted In Degree Distribution (Officer Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted In Degree')

Text(0, 0.5, 'Weighted In Degree')

df_outdegree = pd.DataFrame({'name': list(g_oj.vs['name']), 'weighted_outdegree':g_oj.strength(weights = 'weight', mode = 'out') } )
df_outdegree = df_outdegree.sort_values('weighted_outdegree', ascending = False).reset_index(drop = True)
df_outdegree.head(10)

	name	weighted_outdegree
0	Taiwan	12.5
1	China	9.5
2	Hong Kong	6.0
3	Indonesia	5.0
4	United States	4.5
5	Singapore	2.5
6	India	2.5
7	United Arab Emirates	1.5
8	British Virgin Islands	1.5
9	Japan	1.0

#run cell above before running this always

df_outdegree['weighted_outdegree'].plot()
plt.title('Weighted Out Degree Distribution (All Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Out Degree')

Text(0, 0.5, 'Weighted Out Degree')

df_pagerank = pd.DataFrame({'name': list(g_oj.vs['name']), 'pagerank':g_oj.pagerank(weights = 'weight') } )
df_pagerank = df_pagerank.sort_values('pagerank', ascending = False).reset_index(drop = True)
df_pagerank.head(10)

	name	pagerank
0	British Virgin Islands	0.324553
1	Samoa	0.126458
2	Cook Islands	0.126287
3	Seychelles	0.103840
4	Singapore	0.017466
5	Hong Kong	0.015257
6	Labuan	0.012819
7	New Zealand	0.011883
8	Philippines	0.011883
9	Romania	0.011883

#run cell above before running this always

df_pagerank['pagerank'].plot()
plt.title('Pagerank Distribution (Officer Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Pagerank')

Text(0, 0.5, 'Pagerank')

df_authorities = pd.DataFrame({'name': list(g_oj.vs['name']), 'authority_score':g_oj.authority_score(weights = 'weight') } )
df_authorities = df_authorities.sort_values('authority_score', ascending = False).reset_index(drop = True)
df_authorities.head(10)

	name	authority_score
0	British Virgin Islands	1.000000
1	Samoa	0.066541
2	Labuan	0.035502
3	Hong Kong	0.023994
4	Singapore	0.015414
5	Cook Islands	0.013475
6	Seychelles	0.000076
7	New Zealand	0.000000
8	Philippines	0.000000
9	Romania	0.000000

#run cell above before running this always

df_authorities['authority_score'].plot()
plt.title('Authority Score Distribution (Officer Jurisdiction Relationships)')
plt.xlabel('Countries')
plt.ylabel('Authority Score')

Text(0, 0.5, 'Authority Score')

Community Detection

Label Propogation Community Detection

comm_lp_oj= g_oj.community_label_propagation(weights = 'weight')

ig.plot(comm_lp_oj, mark_groups = True, layout="drl")

modularity = g_oj.modularity(comm_lp_oj, weights='weight')
print(modularity)

0.03795841209829868

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_lp_oj))
print('average degree: ', get_avg_degree(comm_lp_oj))
print('transitivity: ', get_transitivity(comm_lp_oj))
print('diameter: ', get_diameter(comm_lp_oj))

average weighted degree:  [7.8, 1.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [2.8, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [0.5454545454545454, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [2, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Leading Eigenvector Community Detection

comm_leading_eigenvector_oj= g_oj.community_leading_eigenvector(weights = 'weight')

ig.plot(comm_leading_eigenvector_oj, mark_groups = True, layout="drl")

/Users/susankoruthu/opt/anaconda3/lib/python3.8/site-packages/igraph/__init__.py:1281: RuntimeWarning: This method was developed for undirected graphs at src/community/leading_eigenvector.c:530
  membership, _, q = GraphBase.community_leading_eigenvector(

modularity = g_oj.modularity(comm_leading_eigenvector_oj, weights='weight')
print(modularity)

0.10638941398865785

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_leading_eigenvector_oj))
print('average degree: ', get_avg_degree(comm_leading_eigenvector_oj))
print('transitivity: ', get_transitivity(comm_leading_eigenvector_oj))
print('diameter: ', get_diameter(comm_leading_eigenvector_oj))

average weighted degree:  [4.05, 1.0, 0.8333333333333334]
average degree:  [2.1, 1.5, 1.6666666666666667]
transitivity:  [0.018867924528301886, 0.0, 0.0]
diameter:  [2, 1, 2]

df_leading_eigenvector_oj= pd.DataFrame({'name': list(g_oj.vs['name']), 'community':comm_leading_eigenvector_oj.membership } )
df_leading_eigenvector_oj

	name	community
0	British Virgin Islands	0
1	Cook Islands	1
2	Samoa	2
3	Seychelles	0
4	Canada	0
5	Cayman Islands	2
6	China	0
7	Labuan	0
8	Singapore	2
9	Czech Republic	0
10	Fiji	0
11	Hong Kong	0
12	India	2
13	Indonesia	0
14	Italy	1
15	Japan	0
16	Jersey	0
17	Macao	1
18	Malaysia	0
19	Monaco	0
20	New Zealand	0
21	Philippines	0
22	Romania	0
23	South Korea	0
24	Taiwan	0
25	Thailand	2
26	US Virgin Islands	2
27	United Arab Emirates	0
28	United Kingdom	0
29	United States	1

df_leading_eigenvector_oj.describe()

	community
count	30.000000
mean	0.533333
std	0.819307
min	0.000000
25%	0.000000
50%	0.000000
75%	1.000000
max	2.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_leading_eigenvector_oj.membership)):
    vertex_colors.append(colors[comm_leading_eigenvector_oj.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_oj.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_oj.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_oj,'directed_all_jur_images/communities_leading_eigenvector.png', vertex_label = g_oj.vs['name'] , **visual_style)

# Set the layout
my_layout = g_oj.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_oj,'directed_all_jur_images/leading_vector_circular.png', vertex_label = g_oj.vs['name'] , **visual_style)

for i in range(len(comm_leading_eigenvector_oj.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_leading_eigenvector_oj.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_leading_eigenvector_oj.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_leading_eigenvector_oj.subgraphs()[i],'directed_all_jur_images/leading_eigenvector_subgraph' + str(i) + '.png' ,vertex_label = comm_leading_eigenvector_oj.subgraphs()[i].vs['name'],**visual_style  )
    

Spinglass Community Detection

comm_spinglass_oj = g_oj.community_spinglass(weights = 'weight')

ig.plot(comm_spinglass_oj, mark_groups = True, layout="drl")

modularity = g_oj.modularity(comm_spinglass_oj, weights='weight')
print(modularity)

0.10381852551984883

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_spinglass_oj))
print('average degree: ', get_avg_degree(comm_spinglass_oj))
print('transitivity: ', get_transitivity(comm_spinglass_oj))
print('diameter: ', get_diameter(comm_spinglass_oj))

average weighted degree:  [0.5, 1.0, 0.75, 4.05]
average degree:  [1.0, 1.5, 1.5, 2.1]
transitivity:  [nan, 0.0, 0.0, 0.018867924528301886]
diameter:  [1, 1, 1, 2]

df_spinglass_oj = pd.DataFrame({'name': list(g_oj.vs['name']), 'community':comm_spinglass_oj.membership } )
df_spinglass_oj

	name	community
0	British Virgin Islands	3
1	Cook Islands	1
2	Samoa	2
3	Seychelles	3
4	Canada	3
5	Cayman Islands	2
6	China	3
7	Labuan	3
8	Singapore	0
9	Czech Republic	3
10	Fiji	3
11	Hong Kong	3
12	India	2
13	Indonesia	3
14	Italy	1
15	Japan	3
16	Jersey	3
17	Macao	1
18	Malaysia	3
19	Monaco	3
20	New Zealand	3
21	Philippines	3
22	Romania	3
23	South Korea	3
24	Taiwan	3
25	Thailand	2
26	US Virgin Islands	0
27	United Arab Emirates	3
28	United Kingdom	3
29	United States	1

df_spinglass_oj.describe()

	community
count	30.000000
mean	2.400000
std	0.968468
min	0.000000
25%	2.000000
50%	3.000000
75%	3.000000
max	3.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_spinglass_oj.membership)):
    vertex_colors.append(colors[comm_spinglass_oj.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_oj.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_oj.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_oj,'directed_all_jur_images/communities_spinglass.png', vertex_label = g_oj.vs['name'] , **visual_style)

# Set the layout
my_layout = g_oj.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_oj,'directed_all_jur_images/spinglass_circular.png', vertex_label = g_oj.vs['name'] , **visual_style)

for i in range(len(comm_spinglass_oj.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_spinglass_oj.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_spinglass_oj.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_spinglass_oj.subgraphs()[i],'directed_all_jur_images/spinglass_subgraph' + str(i) + '.png' ,vertex_label = comm_spinglass_oj.subgraphs()[i].vs['name'],**visual_style  )
    

Walktrap Community Detection

walktrap_oj = g_oj.community_walktrap(weights = 'weight', steps = 2)

comm_walktrap_oj = walktrap_oj.as_clustering()

ig.plot(comm_walktrap_oj, mark_groups = True, layout="drl")

modularity = g_oj.modularity(comm_walktrap_oj, weights='weight')
print(modularity)

0.03327032136105858

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_walktrap_oj))
print('average degree: ', get_avg_degree(comm_walktrap_oj))
print('transitivity: ', get_transitivity(comm_walktrap_oj))
print('diameter: ', get_diameter(comm_walktrap_oj))

average weighted degree:  [4.074074074074074, 0.6666666666666666]
average degree:  [2.814814814814815, 1.3333333333333333]
transitivity:  [0.09880239520958084, 0.0]
diameter:  [3, 1]

df_walktrap_oj = pd.DataFrame({'name': list(g_oj.vs['name']), 'community':comm_walktrap_oj.membership } )
df_walktrap_oj

	name	community
0	British Virgin Islands	0
1	Cook Islands	1
2	Samoa	0
3	Seychelles	0
4	Canada	0
5	Cayman Islands	0
6	China	0
7	Labuan	0
8	Singapore	0
9	Czech Republic	0
10	Fiji	0
11	Hong Kong	0
12	India	0
13	Indonesia	0
14	Italy	1
15	Japan	0
16	Jersey	0
17	Macao	1
18	Malaysia	0
19	Monaco	0
20	New Zealand	0
21	Philippines	0
22	Romania	0
23	South Korea	0
24	Taiwan	0
25	Thailand	0
26	US Virgin Islands	0
27	United Arab Emirates	0
28	United Kingdom	0
29	United States	0

df_walktrap_oj.describe()

	community
count	30.000000
mean	0.100000
std	0.305129
min	0.000000
25%	0.000000
50%	0.000000
75%	0.000000
max	1.000000

# ##plot community
# visual_style = {}

# vertex_colors = []

# for i in range(len(comm_walktrap_oj.membership)):
#     vertex_colors.append(colors[comm_walktrap_oj.membership[i]])
    
# # Set bbox and margin
# visual_style["bbox"] = (5000,5000)
# visual_style["margin"] = 17

# # Set vertex colours
# visual_style["vertex_color"] = vertex_colors

# # Set edge width
# visual_style["edge_width"] = np.log(g_oj.es['weight']) + 1

# # Set edge color
# visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# # Set vertex size
# visual_style["vertex_size"] = 15

# # Set vertex label size
# visual_style["vertex_label_size"] = 20

# # Set vertex label color
# visual_style["vertex_label_color"] = 'red'

# # Don't curve the edges
# visual_style["edge_curved"] = False

# # Set the layout
# my_layout = g_oj.layout_fruchterman_reingold()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_oj,'directed_all_jur_images/communities_walktrap.png', vertex_label = g_oj.vs['name'] , **visual_style)

# # Set the layout
# my_layout = g_oj.layout_circle()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_oj,'directed_all_jur_images/walktrap_circular.png', vertex_label = g_oj.vs['name'] , **visual_style)

# for i in range(len(comm_walktrap_oj.subgraphs())):
    
#     visual_style["bbox"] = (2000,2000)
#     visual_style["margin"] = 17
    
#     # Set vertex colours
#     visual_style["vertex_color"] = 'green'

#     # Set edge width
#     visual_style["edge_width"] = np.log(comm_walktrap_oj.subgraphs()[i].es['weight']) + 1
#     # Set the layout
#     my_layout = comm_walktrap_oj.subgraphs()[i].layout_fruchterman_reingold()
#     visual_style["layout"] = my_layout

#     ig.plot(comm_walktrap_oj.subgraphs()[i],'directed_all_jur_images/walktrap_subgraph' + str(i) + '.png' ,vertex_label = comm_walktrap_oj.subgraphs()[i].vs['name'],**visual_style  )
    

Infomap Community Detection

comm_infomap_oj = g_oj.community_infomap(edge_weights = 'weight')

ig.plot(comm_infomap_oj, mark_groups = True, layout="drl")

modularity = g_oj.modularity(comm_infomap_oj, weights='weight')
print(modularity)

0.0

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_infomap_oj))
print('average degree: ', get_avg_degree(comm_infomap_oj))
print('transitivity: ', get_transitivity(comm_infomap_oj))
print('diameter: ', get_diameter(comm_infomap_oj))

average weighted degree:  [3.8333333333333335]
average degree:  [2.8]
transitivity:  [0.09863013698630137]
diameter:  [3]

df_infomap_oj = pd.DataFrame({'name': list(g_oj.vs['name']), 'community':comm_infomap_oj.membership } )
df_infomap_oj

	name	community
0	British Virgin Islands	0
1	Cook Islands	0
2	Samoa	0
3	Seychelles	0
4	Canada	0
5	Cayman Islands	0
6	China	0
7	Labuan	0
8	Singapore	0
9	Czech Republic	0
10	Fiji	0
11	Hong Kong	0
12	India	0
13	Indonesia	0
14	Italy	0
15	Japan	0
16	Jersey	0
17	Macao	0
18	Malaysia	0
19	Monaco	0
20	New Zealand	0
21	Philippines	0
22	Romania	0
23	South Korea	0
24	Taiwan	0
25	Thailand	0
26	US Virgin Islands	0
27	United Arab Emirates	0
28	United Kingdom	0
29	United States	0

No Intermediary

df_weighted['status'].unique()

array(['jurisdiction', 'intermediary_base', 'intermediary_jurisdiction',
       'officer_base', 'officer_jurisdiction'], dtype=object)

jurisdiction_list = ['officer_jurisdiction', 'jurisdiction', 'officer_base']

df_weighted_jur = df_weighted[df_weighted['status'].isin(jurisdiction_list)]
df_jur = df_weighted_jur.drop(['status'], axis = 1)
df_jur

	node_start	node_end	weight
0	Hong Kong	Samoa	2.0
1	Hong Kong	Samoa	2.0
2	Hong Kong	Samoa	2.0
3	Hong Kong	Samoa	2.0
4	Hong Kong	Samoa	2.0
...	...	...	...
338119	Indonesia	British Virgin Islands	1.0
338120	Cook Islands	British Virgin Islands	1.0
338121	Hong Kong	British Virgin Islands	1.0
338122	Cook Islands	United Kingdom	1.0
338123	Hong Kong	United Kingdom	1.0

329073 rows × 3 columns

df_jur_grouped = df_jur.groupby(['node_start','node_end'], as_index = False).sum()
df_jur_grouped

	node_start	node_end	weight
0	Albania	Bahamas	4.0
1	Algeria	British Virgin Islands	2.0
2	Algeria	United Kingdom	2.0
3	Algeria	United States	1.0
4	Andorra	Bahamas	52.0
...	...	...	...
2750	Zimbabwe	Hong Kong	3.0
2751	Zimbabwe	Jersey	1.0
2752	Zimbabwe	Panama	6.0
2753	Zimbabwe	Russia	2.0
2754	Zimbabwe	United States	1.0

2755 rows × 3 columns

Convert Data to an Undirected Edge List

# df_jur_grouped_list = df_jur_grouped.values.tolist()
# df_jur_grouped_list

# d = collections.defaultdict(int)
# for n1, n2, v in df_jur_grouped_list:
#     d[min(n1, n2), max(n1, n2)] += v
# result = [[k[0], k[1], v] for k, v in d.items()]

# df_net = pd.DataFrame(result)
# df_net

# df_net = df_net.rename(columns = {0:'node_1', 1:'node_2', 2: 'weight'})
# df_net

#df_net.to_csv('undirected_weighted_grouped.csv', index = False)

# df_net.describe()

Create Graph

g_ni = ig.Graph.TupleList(df_jur_grouped.itertuples(index=False), directed=True, edge_attrs={'weight': "weight"})

ig.plot(g_ni)

g_ni.diameter()

4

print( "Clustering Coefficient: ", g_ni.transitivity_undirected())

Clustering Coefficient:  0.3829243625911535

np.mean(g_ni.degree())

28.256410256410255

np.mean(g_ni.strength(weights = 'weight'))

5595.635897435897

df_strength = pd.DataFrame({'name': list(g_ni.vs['name']), 'weighted_degree':g_ni.strength(weights = 'weight') } )
df_strength = df_strength.sort_values('weighted_degree', ascending = False).reset_index(drop = True)
df_strength.head(10)

	name	weighted_degree
0	British Virgin Islands	283283.5
1	Hong Kong	110569.0
2	Panama	109720.0
3	Switzerland	77116.0
4	Bahamas	40682.0
5	United Kingdom	37265.0
6	Taiwan	33699.5
7	Seychelles	32521.5
8	Jersey	29830.5
9	China	24897.5

#run cell above before running this always

df_strength['weighted_degree'].plot()
plt.title('Weighted Degree Distribution (No Intermediary Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Degree')

Text(0, 0.5, 'Weighted Degree')

df_indegree = pd.DataFrame({'name': list(g_ni.vs['name']), 'weighted_indegree':g_ni.strength(weights = 'weight', mode = 'in') } )
df_indegree = df_indegree.sort_values('weighted_indegree', ascending = False).reset_index(drop = True)
df_indegree.head(10)

	name	weighted_indegree
0	British Virgin Islands	276368.0
1	Panama	89709.0
2	Seychelles	31433.5
3	Bahamas	31079.0
4	Niue	18912.0
5	United Kingdom	15691.0
6	Hong Kong	13566.0
7	Samoa	12487.5
8	Russia	10494.0
9	British Anguilla	6480.0

#run cell above before running this always

df_indegree['weighted_indegree'].plot()
plt.title('Weighted In Degree Distribution (No Intermediary Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted In Degree')

Text(0, 0.5, 'Weighted In Degree')

df_outdegree = pd.DataFrame({'name': list(g_ni.vs['name']), 'weighted_outdegree':g_ni.strength(weights = 'weight', mode = 'out') } )
df_outdegree = df_outdegree.sort_values('weighted_outdegree', ascending = False).reset_index(drop = True)
df_outdegree.head(10)

	name	weighted_outdegree
0	Hong Kong	97003.0
1	Switzerland	76895.0
2	Taiwan	33699.5
3	Jersey	29417.5
4	China	22343.5
5	Luxembourg	21765.0
6	United Kingdom	21574.0
7	Panama	20011.0
8	Singapore	16349.5
9	United States	15964.5

#run cell above before running this always

df_outdegree['weighted_outdegree'].plot()
plt.title('Weighted Out Degree Distribution (No Intermediary Relationships)')
plt.xlabel('Countries')
plt.ylabel('Weighted Out Degree')

Text(0, 0.5, 'Weighted Out Degree')

df_pagerank = pd.DataFrame({'name': list(g_ni.vs['name']), 'pagerank':g_ni.pagerank(weights = 'weight') } )
df_pagerank = df_pagerank.sort_values('pagerank', ascending = False).reset_index(drop = True)
df_pagerank.head(10)

	name	pagerank
0	British Virgin Islands	0.263850
1	Panama	0.128837
2	Barbados	0.080968
3	Bahamas	0.050375
4	Hong Kong	0.046558
5	United Kingdom	0.046447
6	Seychelles	0.037883
7	Russia	0.031472
8	Niue	0.028551
9	Bermuda	0.016875

#run cell above before running this always

df_pagerank['pagerank'].plot()
plt.title('Pagerank Distribution (No Intermediary Relationships)')
plt.xlabel('Countries')
plt.ylabel('Pagerank')

Text(0, 0.5, 'Pagerank')

df_authorities = pd.DataFrame({'name': list(g_ni.vs['name']), 'authority_score':g_ni.authority_score(weights = 'weight') } )
df_authorities = df_authorities.sort_values('authority_score', ascending = False).reset_index(drop = True)
df_authorities.head(10)

	name	authority_score
0	British Virgin Islands	1.000000
1	Panama	0.207994
2	Seychelles	0.103974
3	Bahamas	0.070005
4	Samoa	0.063105
5	Niue	0.056301
6	United Kingdom	0.039640
7	British Anguilla	0.027027
8	Russia	0.026683
9	Hong Kong	0.015784

#run cell above before running this always

df_authorities['authority_score'].plot()
plt.title('Authority Score Distribution (No Intermediary Relationships)')
plt.xlabel('Countries')
plt.ylabel('Authority Score')

Text(0, 0.5, 'Authority Score')

Community Detection

Label Propogation Community Detection

comm_lp_ni= g_ni.community_label_propagation(weights = 'weight')

ig.plot(comm_lp_ni, mark_groups = True, layout="drl")

modularity = g_ni.modularity(comm_lp_ni, weights='weight')
print(modularity)

0.0012668163862697814

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_lp_ni))
print('average degree: ', get_avg_degree(comm_lp_ni))
print('transitivity: ', get_transitivity(comm_lp_ni))
print('diameter: ', get_diameter(comm_lp_ni))

average weighted degree:  [0.0, 13317.28, 0.0, 0.0, 84.0, 0.0, 0.0, 18.0, 0.0, 0.0, 230.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 16.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 44.16, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.6641905218336989, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 3, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Leading Eigenvector Community Detection

comm_leading_eigenvector_ni= g_ni.community_leading_eigenvector(weights = 'weight')

ig.plot(comm_leading_eigenvector_ni, mark_groups = True, layout="drl")

/Users/susankoruthu/opt/anaconda3/lib/python3.8/site-packages/igraph/__init__.py:1281: RuntimeWarning: This method was developed for undirected graphs at src/community/leading_eigenvector.c:530
  membership, _, q = GraphBase.community_leading_eigenvector(

modularity = g_ni.modularity(comm_leading_eigenvector_ni, weights='weight')
print(modularity)

0.14956936235767823

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_leading_eigenvector_ni))
print('average degree: ', get_avg_degree(comm_leading_eigenvector_ni))
print('transitivity: ', get_transitivity(comm_leading_eigenvector_ni))
print('diameter: ', get_diameter(comm_leading_eigenvector_ni))

average weighted degree:  [3397.7586206896553, 4895.692307692308, 0.0, 0.0, 0.0, 1.0, 0.0, 16.0, 0.0]
average degree:  [8.206896551724139, 23.53846153846154, 0.0, 0.0, 0.0, 1.0, 0.0, 2.0, 0.0]
transitivity:  [0.27990271943400397, 0.44260359931244436, nan, nan, nan, nan, nan, nan, nan]
diameter:  [3, 3, 0, 0, 0, 1, 0, 0, 0]

df_leading_eigenvector_ni= pd.DataFrame({'name': list(g_ni.vs['name']), 'community':comm_leading_eigenvector_ni.membership } )
df_leading_eigenvector_ni

	name	community
0	Albania	0
1	Bahamas	0
2	Algeria	1
3	British Virgin Islands	1
4	United Kingdom	1
...	...	...
190	Venezuela	0
191	Vietnam	1
192	Yemen	0
193	Zambia	1
194	Zimbabwe	1

195 rows × 2 columns

df_leading_eigenvector_ni.describe()

	community
count	195.000000
mean	0.928205
std	1.076925
min	0.000000
25%	0.000000
50%	1.000000
75%	1.000000
max	8.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_leading_eigenvector_ni.membership)):
    vertex_colors.append(colors[comm_leading_eigenvector_ni.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_ni.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_ni.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_ni,'directed_all_jur_images/communities_leading_eigenvector.png', vertex_label = g_ni.vs['name'] , **visual_style)

# Set the layout
my_layout = g_ni.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_ni,'directed_all_jur_images/leading_vector_circular.png', vertex_label = g_ni.vs['name'] , **visual_style)

for i in range(len(comm_leading_eigenvector_ni.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_leading_eigenvector_ni.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_leading_eigenvector_ni.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_leading_eigenvector_ni.subgraphs()[i],'directed_all_jur_images/leading_eigenvector_subgraph' + str(i) + '.png' ,vertex_label = comm_leading_eigenvector_ni.subgraphs()[i].vs['name'],**visual_style  )
    

Spinglass Community Detection

comm_spinglass_ni = g_ni.community_spinglass(weights = 'weight')

ig.plot(comm_spinglass_ni, mark_groups = True, layout="drl")

modularity = g_ni.modularity(comm_spinglass_ni, weights='weight')
print(modularity)

0.054326644420026556

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_spinglass_ni))
print('average degree: ', get_avg_degree(comm_spinglass_ni))
print('transitivity: ', get_transitivity(comm_spinglass_ni))
print('diameter: ', get_diameter(comm_spinglass_ni))

average weighted degree:  [1283.1864406779662, 1465.157894736842, 798.6315789473684, 2070.9411764705883, 1798.0, 126.42857142857143, 313.6, 844.0, 230.0]
average degree:  [3.4237288135593222, 4.947368421052632, 11.631578947368421, 3.823529411764706, 4.2727272727272725, 2.4285714285714284, 2.0, 1.0, 1.0]
transitivity:  [0.06727099236641221, 0.39, 0.4916555407209613, 0.1836734693877551, 0.36401673640167365, 0.11392405063291139, 0.0, nan, nan]
diameter:  [3, 3, 3, 4, 3, 2, 1, 1, 1]

df_spinglass_ni = pd.DataFrame({'name': list(g_ni.vs['name']), 'community':comm_spinglass_ni.membership } )
df_spinglass_ni

	name	community
0	Albania	1
1	Bahamas	1
2	Algeria	2
3	British Virgin Islands	0
4	United Kingdom	2
...	...	...
190	Venezuela	3
191	Vietnam	0
192	Yemen	3
193	Zambia	0
194	Zimbabwe	0

195 rows × 2 columns

df_spinglass_ni.describe()

	community
count	195.000000
mean	2.128205
std	1.901972
min	0.000000
25%	0.000000
50%	2.000000
75%	3.000000
max	8.000000

##plot community
visual_style = {}

vertex_colors = []

for i in range(len(comm_spinglass_ni.membership)):
    vertex_colors.append(colors[comm_spinglass_ni.membership[i]])
    
# Set bbox and margin
visual_style["bbox"] = (5000,5000)
visual_style["margin"] = 17

# Set vertex colours
visual_style["vertex_color"] = vertex_colors

# Set edge width
visual_style["edge_width"] = np.log(g_ni.es['weight']) + 1

# Set edge color
visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# Set vertex size
visual_style["vertex_size"] = 15

# Set vertex label size
visual_style["vertex_label_size"] = 20

# Set vertex label color
visual_style["vertex_label_color"] = 'red'

# Don't curve the edges
visual_style["edge_curved"] = False

# Set the layout
my_layout = g_ni.layout_fruchterman_reingold()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_ni,'directed_all_jur_images/communities_spinglass.png', vertex_label = g_ni.vs['name'] , **visual_style)

# Set the layout
my_layout = g_ni.layout_circle()
visual_style["layout"] = my_layout

# Plot the graph
ig.plot(g_ni,'directed_all_jur_images/spinglass_circular.png', vertex_label = g_ni.vs['name'] , **visual_style)

for i in range(len(comm_spinglass_ni.subgraphs())):
    
    visual_style["bbox"] = (2000,2000)
    visual_style["margin"] = 17
    
    # Set vertex colours
    visual_style["vertex_color"] = 'green'

    # Set edge width
    visual_style["edge_width"] = np.log(comm_spinglass_ni.subgraphs()[i].es['weight']) + 1
    # Set the layout
    my_layout = comm_spinglass_ni.subgraphs()[i].layout_fruchterman_reingold()
    visual_style["layout"] = my_layout

    ig.plot(comm_spinglass_ni.subgraphs()[i],'directed_all_jur_images/spinglass_subgraph' + str(i) + '.png' ,vertex_label = comm_spinglass_ni.subgraphs()[i].vs['name'],**visual_style  )
    

Walktrap Community Detection

walktrap_ni = g_ni.community_walktrap(weights = 'weight', steps = 2)

comm_walktrap_ni = walktrap_ni.as_clustering()

ig.plot(comm_walktrap_ni, mark_groups = True, layout="drl")

modularity = g_ni.modularity(comm_walktrap_ni, weights='weight')
print(modularity)

0.002879845289073743

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_walktrap_ni))
print('average degree: ', get_avg_degree(comm_walktrap_ni))
print('transitivity: ', get_transitivity(comm_walktrap_ni))
print('diameter: ', get_diameter(comm_walktrap_ni))

average weighted degree:  [0.0, 8642.008064516129, 0.0, 0.0, 54.285714285714285, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 16.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
average degree:  [0.0, 37.903225806451616, 0.0, 0.0, 1.7142857142857142, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
transitivity:  [nan, 0.4614273777519436, nan, nan, 0.0, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
diameter:  [0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

df_walktrap_ni = pd.DataFrame({'name': list(g_ni.vs['name']), 'community':comm_walktrap_ni.membership } )
df_walktrap_ni

	name	community
0	Albania	0
1	Bahamas	1
2	Algeria	2
3	British Virgin Islands	1
4	United Kingdom	1
...	...	...
190	Venezuela	1
191	Vietnam	1
192	Yemen	63
193	Zambia	64
194	Zimbabwe	65

195 rows × 2 columns

df_walktrap_ni.describe()

	community
count	195.000000
mean	11.753846
std	18.576144
min	0.000000
25%	1.000000
50%	1.000000
75%	16.500000
max	65.000000

# ##plot community
# visual_style = {}

# vertex_colors = []

# for i in range(len(comm_walktrap_ni.membership)):
#     vertex_colors.append(colors[comm_walktrap_ni.membership[i]])
    
# # Set bbox and margin
# visual_style["bbox"] = (5000,5000)
# visual_style["margin"] = 17

# # Set vertex colours
# visual_style["vertex_color"] = vertex_colors

# # Set edge width
# visual_style["edge_width"] = np.log(g_ni.es['weight']) + 1

# # Set edge color
# visual_style["edge_color"] = "rgba(1,1,1,0.1)" 

# # Set vertex size
# visual_style["vertex_size"] = 15

# # Set vertex label size
# visual_style["vertex_label_size"] = 20

# # Set vertex label color
# visual_style["vertex_label_color"] = 'red'

# # Don't curve the edges
# visual_style["edge_curved"] = False

# # Set the layout
# my_layout = g_ni.layout_fruchterman_reingold()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_ni,'directed_all_jur_images/communities_walktrap.png', vertex_label = g_ni.vs['name'] , **visual_style)

# # Set the layout
# my_layout = g_ni.layout_circle()
# visual_style["layout"] = my_layout

# # Plot the graph
# ig.plot(g_ni,'directed_all_jur_images/walktrap_circular.png', vertex_label = g_ni.vs['name'] , **visual_style)

# for i in range(len(comm_walktrap_ni.subgraphs())):
    
#     visual_style["bbox"] = (2000,2000)
#     visual_style["margin"] = 17
    
#     # Set vertex colours
#     visual_style["vertex_color"] = 'green'

#     # Set edge width
#     visual_style["edge_width"] = np.log(comm_walktrap_ni.subgraphs()[i].es['weight']) + 1
#     # Set the layout
#     my_layout = comm_walktrap_ni.subgraphs()[i].layout_fruchterman_reingold()
#     visual_style["layout"] = my_layout

#     ig.plot(comm_walktrap_ni.subgraphs()[i],'directed_all_jur_images/walktrap_subgraph' + str(i) + '.png' ,vertex_label = comm_walktrap_ni.subgraphs()[i].vs['name'],**visual_style  )
    

Infomap Community Detection

comm_infomap_ni = g_ni.community_infomap(edge_weights = 'weight')

ig.plot(comm_infomap_ni, mark_groups = True, layout="drl")

modularity = g_ni.modularity(comm_infomap_ni, weights='weight')
print(modularity)

0.0

#get metrics for each community

print('average weighted degree: ', get_avg_weighted_degree(comm_infomap_ni))
print('average degree: ', get_avg_degree(comm_infomap_ni))
print('transitivity: ', get_transitivity(comm_infomap_ni))
print('diameter: ', get_diameter(comm_infomap_ni))

average weighted degree:  [5595.635897435897]
average degree:  [28.256410256410255]
transitivity:  [0.3829243625911535]
diameter:  [4]

df_infomap_ni = pd.DataFrame({'name': list(g_ni.vs['name']), 'community':comm_infomap_ni.membership } )
df_infomap_ni

	name	community
0	Albania	0
1	Bahamas	0
2	Algeria	0
3	British Virgin Islands	0
4	United Kingdom	0
...	...	...
190	Venezuela	0
191	Vietnam	0
192	Yemen	0
193	Zambia	0
194	Zimbabwe	0

195 rows × 2 columns